Calculus BC Trigonometric Identities, Derivatives, and Integrals

sin² x + cos² x

1

1 + cot² x

csc² x

tan² x + 1

sec² x

tan x

sin x/cos x

cot x

cos x/sin x

d(sin x)/dx

cos x

d(cos x)/dx

−sin x

d(tan x)/dx

sec² x

d(cot x)/dx

−csc² x

d(sec x)/dx

sec x tan x

d(csc x)/dx

−csc x cot x

∫cos x dx

sin x + C

∫sin x dx

−cos x + C

∫sec² x dx

tan x + C

∫csc² x dx

−cot x + C

∫sec x tan x dx

sec x + C

∫csc x cot x dx

−csc x + C

∫tan x dx

−ln |cos x| + C

∫cot x dx

ln |sin x| + C

∫sec x dx

ln |sec x tan x| + C

∫csc x dx

−ln |csc x cot x| + C

∫du/√(a² − u²)

arcsin(u/a) + C

∫du/(a² + u²)

1/a arctan(u/a) + C

∫du/(|u| √(u² − a²))

1/a arcsec(|u|/a) + C

d(arcsin x)/dx

1/√(1 − x²)

d(arccos x)/dx

−1/√(1 − x²)

d(arcsec x)/dx

1/(|x| √(x² − 1))

d(arccsc x)/dx

−1/(|x| √(x² − 1))

d(arctan x)/dx

1/(1 + x²)

d(arccot x)/dx

−1/(1 + x²)